Further Results on Resistance Distance and Kirchhoff Index in Electric Networks

In electric circuit theory, it is of great interest to compute the effective resistance between any pairs of vertices of a network, as well as the Kirchhoff index. Let be the graph obtained from by inserting a new vertex into every edge of and by joining by edges those pairs of these new vertices which lie on adjacent edges of . The set of such new vertices is denoted by . The -vertex corona of and , denoted by , is the graph obtained from vertex disjoint and copies of by joining the th vertex of to every vertex in the th copy of . The -edge corona of and , denoted by , is the graph obtained from vertex disjoint and copies of by joining the th vertex of to every vertex in the th copy of . The objective of the present work is to obtain the resistance distance and Kirchhoff index for composite networks such as -vertex corona and -edge corona networks.